It is well known that both chains are reversible with respect to \(\mu \)  [1]}.
Both chains can be defined for general (not necessarily Gibbs) distributions \(\mu \)  over \(Q^V\) ,
by setting \(G\)  as the complete graph and hence the marginal distributions \(\mu _v^{\tau _{N_v}}=\mu _v^{\tau _{V\setminus \lbrace v\rbrace }}\) .
